We have found that the application of a weak radio frequency (rf) pulse to a spin system with indirect spin-spin (J) couplings can produce a narrow inverted peak in spectral regions where there are many overlapping peaks. Examples of three compounds with H-1-H-1 J couplings and one with H-1-C-13 J couplings are given. The dependences of the signals on the frequency, duration, and amplitude of the weak rf irradiation have been studied. For an rf power of gammaB(1)/2pi=1.0 Hz, pulse widths longer than 0.25 s consistently produce inverted narrow peaks in spectral regions with unresolved peaks. An interpretation of the origin of this unusual result of selective excitation in spin systems with homogeneous broadening is given: the inverted signal observed can be considered as a cumulative effect of the weak rf irradiation acting on many uncorrelated transitions that are slightly off resonance on both sides of the irradiating frequency; the only role of the J couplings (or dipolar couplings in liquid crystals) is to produce a large number of closely spaced peaks that overlap with each other. Computer simulations of both coupled and noninteracting spin systems have been carried out, and the results support this interpretation. (C) 2004 American Institute of Physics.